Methods of estimating the dimensional stability of a wood product from simple algebraic functions of moisture, shrinkage rates and grain angles

ABSTRACT

Methods are provided for estimating the dimensional stability of a wood product from simple algebraic functions of moisture, shrinkage rates and grain angles observed on outer surfaces. The methods may employ single or multiple sensor group measurements. The quantitative relationship between crook or bow stability and lengthwise shrinkage can be established using mathematical operations, rather than sophisticated and complicated finite-element modeling methods. In particular, the curvature of any board length-segment or section, expressed as the second derivative of the crook or bow profile, can be determined from a linear combination of the shrinkage values of the coupons including that segment or section. The overall crook or bow profile of the board can be determined from a section-by-section double-integration of those second derivative values.

FIELD OF THE INVENTION

The present invention generally relates to the use of single andmultiple sensor group systems to infer qualitative and/or quantitativeestimates of various properties of wood products, including dimensionalstability.

BACKGROUND OF THE INVENTION

Wood products, such as logs, boards, other lumber products, or the like,can be graded or classified into qualitative groups by the amount ofwarp potential, or dimensional stability, in the product. Crook, bow,twist, and cup are examples of warp and are illustrated in FIG. 1. Thegroups are used to qualitatively represent the warp state at a specifiedambient condition or the degree of warp instability of a wood product.The qualitative groups are typically ordinal in nature, though nominalcategories may also be used.

Examples of qualitative estimates of warp might be, but are not limitedto, low crook, high crook, crook less than 0.5 inches but greater than0.25 inches, medium bow, bow greater than 1 inch, or like estimates. Itmight be desirable to classify the warp distortion that a wood productwill undergo after it is remanufactured, its moisture redistributes, orit is placed in a new relative humidity environment. Examples of theseclassifications might be, but are not limited to, low crook at 20% RH,medium crook at 65% RH, high bow at 90% RH, crook greater than 0.5inches at 20% RH. Wood products can also be characterized in aquantitative manner, such as, an amount of change a wood product willundergo (i.e., crook equal to 0.25 inches). Several known methods fordetermining quantitative estimates are described below.

The degree of warp depends on several known factors, such as density,modulus of elasticity (hereinafter referred to as “MOE”), moisturecontent variation, pith location, compression wood, grain angle andothers. Many of these factors can be quantitatively or qualitativelyevaluated with different types of sensors. For example, MOE can beestimated from the propagation of sound through wood, and specificgravity can be estimated from the capacitance of wood. A different typeof sensor group or system may be utilized for detecting each of theseproperties.

During the three year period from 1995 to 1998, solid sawn softwoodlumber usage in wall framing, floor framing and roof framing dropped by9.9%, 17.2% and 11% respectively in the United States (Eastin et al.,2001)¹. In this survey of nearly 300 builders, lumber straightness wasrated the most important factor affecting buying decisions; yet of allthe quality attributes surveyed, dissatisfaction with straightness washighest. It is generally recognized that softwood lumber will continueto lose market share unless the industry improves the in-service warpstability of its product. ¹Eastin, I. L., Shook, S. R., Fleishman, S.J., Material substitution in the U.S. residential construction industry,1994 versus 1988, Forest Products Journal, Vol. 51, No. 9, 31-37.

Some wood product applications are intolerant of significant dimensionalchange (thickness, width, length) after the product is put in service.For example, instability of thickness or width dimensions can causeinterference problems for tight-tolerance applications, such as doorsand windows. Length instability of wood used in truss chords can resultin a problem known as truss uplift; where the truss can raise aboveinterior wall plates forming a gap between the ceiling and interiorwall.

In the United States, most softwood dimension lumber is visually gradedfor a variety of attributes that affect its appearance and structuralproperties. These attributes include knots, wane, dimension (thickness,width, and length), decay, splits and checks, slope-of-grain, andstraightness (warp). Strict quality control practices overseen by thirdparty grading agencies are in place to ensure that all lumber is“on-grade” at the point the grade is assigned. Unfortunately, thestraightness and dimension of a piece are not static and can changeafter the piece is graded. Additional warp and size change can developafter the piece is in the distribution channel or after it is put intoservice. Typical moisture content of fresh kiln dried lumber averages15% but ranges from 6% to 19%. This lumber will eventually equilibratedto a moisture ranging from 3% to 19% depending on time of year,geography and whether the application is interior or exterior (WoodHandbook)². This moisture change results in changes in both dimensionand warp properties. Any piece of lumber is prone to develop additional“in-service” warp if a) its shrinkage properties are not uniform and itchanges moisture or b) its moisture content is not uniform at the pointthe original grade was assigned. Neither of these conditions isdetectable with traditional visual grading methods. Customers of woodproducts seek stability in both dimension and warp properties. ²WoodHandbook, General Technical Report 113 (1999) Department of Agriculture,Forest Service, Forest Products Laboratory.

The wood handbook² provides guidelines for assessing the width andthickness stability of solid sawn lumber. Average thickness and widthshrinkage is governed by grain orientation as well as radial andtangential shrinkage properties. These average radial and tangentialshrinkage values vary by species and are reduced if heartwood ispresent. Although these methods can be used to estimate the averagethickness and width shrinkage behavior of a species, methods for precisequantification do not exist. There are even fewer design tools forestimating length shrinkage.

A number of studies (e.g. Johansson, 2002³ and Beard et al., 1993⁴) haveattempted to define visual indicators that correlate with warpstability. Candidate indicators have included features such as percentjuvenilewood, grain orientation, compressionwood, pith location, wane,knot properties and growth rate. Although these studies demonstrate thatspiral grain can be a useful predictor of twist stability, theygenerally agree that there are no reliable visual indicators of crookand bow stability. ³Johansson, M., and Kliger, R., Influence of materialcharacteristics on warp in Norway Spruce studs, Wood and Fiber Science,34(2). 2002, pp 325-336, 2002 by the Society of Wood Science andTechnology ⁴Beard, J. S., Wagner, F. G., Taylor, F. W., Seale, R. D.,The influence of growth characteristics on warp in two structural gradesof southern pine lumber, Forest Products Journal, Vol. 43, No. 6, pp51-56.

Several theoretical models have also been developed to help explain howmoisture and various wood properties interact to cause distortion.Nearly fifty years ago, a mathematical model was developed to explainlumber twist as a function of spiral grain angle, distance from pith,and rate of tangential shrinkage during moisture loss (Stevens et al.,1960⁵). Other recent work has sought to develop finite element models topredict crook and bow distortion (Ormarsson et al., 1998⁶) as a functionof three-dimensional patterns of density, growth rings, moisture,modulus of elasticity, etc. Another finite element model is described ina series of U.S. Pat. (Nos. 6,308,571; 6,305,224; and 6,293,152) toStanish et al. All of these models teach that the fundamental cause oflumber warp is related to the fact that it shrinks significantly when itdries and this shrinkage is both anisotropic and highly non-uniform.Prediction of warp stability of a wood product is made even moredifficult by the fact that its moisture content changes with the vapourpressure of the surrounding environment and this “equilibrium moisture”can be highly variable between two locations within a piece depending onthe chemistry and fibre differences between those two locations.⁵Stevens, W. C., and Johnston, D. D., Distortion caused by spiralledgrain, Timber Technology, Jun. 1960, pp 217-218.⁶Ormarsson, S.,Dahlblom, O., Petersson, H., A numerical study of the shape stability ofsawn timber subjected to moisture variation, Wood Science and Technology32 (1988) 325-334, Springer-Verlag 1998.

Today the patterns of equilibrium moisture and shrinkage coefficientswithin a full size lumber product can be accurately measured only in alaboratory environment. The laboratory technique involves cutting thepiece of lumber into small “coupons” and measuring the moisture contentand shrinkage coefficients using ASTM standards D-4492 and D-143,respectively. Although much is known about equilibrium moisture andshrinkage behavior of wood, there are as yet no comprehensivetheoretical models and no methods of monitoring these properties in areal time production environment.

Much of the fundamental research to develop shrinkage models for woodwas done several decades ago. Shrinkage is known to be related tomicrofibril angle (Meylan, 1968⁷). This relationship is best wheremicrofibril angle is in the range of 30° to 40° and outside this range,the relationship is rather poor. Wooten (Wooten, 1967⁸) observed thatlongitudinal shrinkage of high microfibril angle wood (>40 degrees) inseedlings seemed to correlate with the thickness of the S₁layer—although no data was presented. Cave (Cave, 1972⁹) proposed ashrinkage theory which includes effects of the S₁ layer. More recently,Floyd (Floyd, 2005¹⁰) demonstrated that certain hemicellulosecomponents, particularly galactan, interact with microfibrils to affectlongitudinal shrinkage rates. This combined work suggests thatmeasurements relating to microfibril angle and wood hemicellulosechemistry should be useful in predicting shrinkage patterns in wood.⁷Meylan, B. A., Cause of high longitudinal shrinkage in wood, ForestProducts Journal, Vol. 18, No. 4, Apr. 1968, pp 75-78.⁸Wooten, T. E.,Barefoot, A. C., and Nicholas, D. D., The longitudinal shrinkage ofcompression wood, Holzforschung. Bd. 21 (1967), Heft 6, pp168-171.⁹Cave, I. D., A theory of the shrinkage of wood. Wood Sci. Tech(1972), 6:284-292.¹⁰Floyd, S. “Effect of Hemicellulose on LongitudinalShrinkage in Wood.” In The Hemicellulloses Workshop 2005: WQILimited—New Knowledge in Wood Quality. Conference held in The WoodTechnology Research Centre. University of Canterbury New Zealand. 10-12Jan. 2005, edited by Kenneth M. Entwistle and John C. F. Walker, 115-.Christchurch, New Zealand, 2005.

Several researchers have recently reported some success using theseapproaches to estimate shrinkage properties. The above referencedpatents issued to Stanish et al. teach a method of inferring shrinkagebehavior by interpreting patterns of acoustic or ultrasound propagationvelocity (related to microfibril angle). Several recent patents andpublications have begun to disclose methods of estimating shrinkagecoefficients which are more compatible with a high speed lumbermanufacturing process. For example, Nystom (Nystrom et al.¹¹)demonstrated the relationship between longitudinal shrinkage and anoptical property of wood (“tracheid-effect”) that is also related tomicrofibril angle. The “tracheid effect” is taught in U.S. Pat. No.3,976,384 issued to Matthews et al. A large number of recentpublications and patents (e.g. Kelley et al.¹²) teach a method ofinferring shrinkage properties by using chemometric methods of nearinfrared spectroscopy (NIRS). NIRS is of particular interest because themethod is sensitive to both physical attributes of the fibres (e.g.microfibrils) and chemical attributes (e.g. hemicellulose). ¹¹Nystrom,J.; Hagman, O.; Methods for detecting compression wood in green and dryconditions., Proceedings of the SPIE—The International Society forOptical Engineering (1999) vol. 3826, p. 287-94.¹²Kelley, S.; Rials, T.;Snell, R.; Groom, L.; Sluiter, A; Wood Science and Technology (2004),38(4), 257-276

Unfortunately, none of the individual methods described above areaccurate enough to give adequate estimates of the dimensional stabilityof a single piece of lumber. Thus, a need exists for the use of singleor multiple sensor systems to provide a qualitative and/or quantitativeestimate of the current or future warp distortion of the wood product orof warp-related properties of the wood product.

BRIEF DESCRIPTION OF THE DRAWINGS

The embodiments of the present invention are described in detail belowwith reference to the following drawings:

FIG. 1 provides examples of crook, bow, twist, and cup in a woodproduct;

FIG. 2 is a plot of misclassified boards in an embodiment of the presentinvention;

FIG. 3 is a plot of misclassified boards in an embodiment of the presentinvention;

FIG. 4 is a calibration plot for a differential shrinkage-coefficientmodel in an embodiment of the present invention;

FIG. 5 is a plot of predicted change in crook against the measuredchange in an embodiment of the present invention;

FIG. 6 is a chart of different initial moisture content profiles;

FIG. 7 is a chart of predicted crook changes for each profile in FIG. 6;

FIG. 8 is a plot of moisture content profiles at different depths;

FIG. 9 is a plot of predicted moisture content for a wood product in anembodiment of the present invention;

FIG. 10 is a plot comparing the second derivative values calculatedusing a method of the present invention with the corresponding secondderivative values calculated from the crook profiles predicted by thefinite-element model;

FIG. 11 is a plot of crook values calculated using a method of thepresent invention compared to corresponding crook values predicted usinga finite-element model;

FIG. 12 is a plot comparing second derivative values calculated using amethod of the present invention with corresponding second derivativevalues calculated from bow profiles predicted by a finite-element model;

FIG. 13 is a plot of bow values calculated using a method of the presentinvention compared to corresponding crook values predicted using afinite-element model;

FIG. 14 is an example of a grayscale image from a line-light-sourceprojected onto a wood product;

FIG. 15 provides several examples of a bi-exponential model fit totracheid-effect line images;

FIG. 16 is a calibration plot for a differential shrinkage-coefficientmodel;

FIG. 17 is a calibration plot for absolute-crook at 20% RH;

FIG. 18 is a plot of a comparison between shrinkage-coefficientestimates;

FIG. 19 is a plot of spectra for wood products based on whether the woodproducts contain pitch;

FIG. 20 is a plot of measured and predicted shrinkage values plottedagainst fitted values; and

FIG. 21 is a plot of measured strain difference versus predicted straindifference.

DETAILED DESCRIPTION OF THE INVENTION

The present invention generally relates to a variety of methods forobtaining and validating improved estimates of shrinkage patterns,moisture patterns and warp stability for a wood product. The term “woodproduct” may be interpreted to mean a board, log, other type of lumber,or the like. The methods involve the use of single and/or multiplesensor group systems to provide qualitative and/or quantitativeestimates. It has been discovered that estimates of dimensionalstability can be much improved when an assortment of measurements areused together, where each measurement contributes information relatingto one or more variables. The measurements may be taken at one or moresections of the wood product, which may differ in size given aparticular embodiment. The properties observed at the one or moresections may allow a qualitative and/or quantitative estimate ofdimensional stability of a region of interest. In a first embodiment,the region of interest may be a coupon or other portion of the woodproduct. In another embodiment, the region of interest may overlap withone or more sections of the wood product. In another embodiment, theregion of interest may be the entire wood product. In yet anotherembodiment, the region of interest may be the same as the one or moresections detected by the sensor group(s). In another embodiment, theregion of interest does not have an overlap with the one or moresections. The dimensional stability assessed may be cup, crook, bow,twist, length stability, thickness stability, width stability, or anycombination of these. Provided below are various embodiments of thepresent invention:

A. Methods of Using Multiple Sensors (Sensor Fusion) to ProvideQualitative and/or Quantitative Assessments via Analysis of Regions ofInterest in a Wood Product Where Non-Uniformity of Composition (e.g.Moisture), Shrinkage Rate or Grain Angle May Result in warp Instabilityof the Wood Product

In an embodiment of the present invention, a classification algorithmmay be created to classify a wood product into one of a plurality ofgroups or categories. The groups may be based on qualitative orquantitative characteristics. For example, in an embodiment, thecategories may be different grades. Warp classification of woodproducts, such as boards may require inputs from one or more sensorgroups detecting properties of the boards. The sensor groups may be apart of those systems previously mentioned for analyzing a wood product.The technologies for these systems are known by those skilled in theart. For example, the sensor groups may obtain moisture contentmeasurement, electrical property measurement, structural propertymeasurement, acousto-ultrasonic property measurement, light scatter(tracheid-effect) measurement, grain angle measurement, shapemeasurement, color measurement, spectral measurement and/or defect maps.Structural property measurement may measure modulus of elasticity,density, specific gravity, strength, or a combination of these.Acousto-ultrasonic property measurement measures may measure velocityand/or damping. The spectral measurement may be characterized byabsorption or reflectance values over a wavelength spectrum ranging fromultraviolet through near infrared.

Using this approach, the prediction model or algorithm of the presentinvention may use inputs of many different resolution scales. Someexamples are board average MOE, moisture content measured across thewidth of the board in one foot increments along the length of the board,spectroscopy data collected every inch, or laser data collected every ¼inch.

The inputs are functions of the sensor signals and may be eitherquantitative or qualitative. For example, an input could be theestimated moisture content for each 12 inch lineal section of a piece oflumber, as estimated by a moisture meter. Another example is anindicator for the presence or absence of a knot in a 12 inch by 1 inchsection of wood, based on a color image. Inputs may be direct sensormeasurements, pre-processed signals, combined signals from severalsensors or predicted measures from other sensors. Signal pre-processingmay include, but is not limited to, such steps as filtering, smoothing,derivative calculations, power spectrum calculations, Fouriertransforms, etc., as is well known in the art. Predicted measurementsfrom other sensors may include, but are not limited to,shrinkage-coefficients predicted from sensors which measure the lightscattering and light absorption properties of wood and used as inputs toa partial least squares, or “PLS”, prediction model.

The prediction algorithm(s) or model(s) based on the set of inputs canbe derived using many techniques which include, but are not limited to,regression trees, classification trees, linear discriminant analysis,quadratic discriminant analysis, logistic regression, Partial LeastSquares or other supervised learning techniques such as neural networks.There are many forms of equations or algorithms that could be used, anda general reference is Hastie, et al¹³. ¹³Hastie, T., Tibshirani, R.,and Friedman, J., (2001) The Elements of Statistical Learning, Springer,N.Y.

These algorithms can be developed to classify boards into 2 or moregroups. For example, boards might be classified into four grades (#1grade, #2 grade, #3 grade, #4 grade) or into two classifications (warpand no warp), or into three categories (crook less than 0.25 inches,crook between 0.25 and 0.5 inches, crook greater than 0.5 inches).Typically, the parameters in the models or algorithms are derived from atraining-set of data and the performance is tested on a testing-set ofdata before being used in production, although other approaches exist.

Various embodiments are contemplated involving the use of sensor groupsand algorithms. In a first embodiment, a single sensor group may provideinputs to a classification algorithm which classifies wood products intoone of a plurality of groups or categories, such as grades, for example.

In a second embodiment, a single sensor group may provide inputs to aclassification algorithm as in the previous example. However, in thisembodiment, a second algorithm may be selected after classifying thewood product. This second algorithm may be selected from a plurality ofalgorithms which are used to assess the dimensional stability in aquantitative manner.

In a third embodiment, two or more sensor groups may provide two or moreinputs to a classification algorithm to classify wood products into oneof a plurality of categories.

In a fourth embodiment, two or more sensor groups may provide two ormore inputs to an algorithm for providing a quantitative assessment ofdimensional stability of wood products.

In a fifth embodiment, two or more sensor groups may provide two or moreinputs to a classification algorithm to classify wood products into oneof a plurality of categories. Next, a second algorithm may be selectedafter classifying the wood product. This second algorithm may beselected from a plurality of algorithms which are used to assess thedimensional stability in a quantitative manner.

The following example illustrates how information from multiple sensorswas used to predict a warp classification for lumber.

EXAMPLE 1

Three groups of lumber, each containing approximately 200 8-foot long 2inch by 4 inch boards, were obtained from a mill. Via the use ofmultiple sensors, each piece of lumber was measured for crook, bow,average moisture content, ultrasonic velocity and a density profile wasobtained. Each piece of wood was then placed in a 20% relative humidity,or “RH” environment for 5 weeks and then measured again for crook andbow. In this example, the objective was to classify the boards into twofinal warp classes (at 20% RH) using the initial data from multiplesensors. The final warp classes were defined as follows: a board wasclassified as a “rogue” if the absolute crook at 20% RH was greater than0.5 inches or the absolute bow at 20% RH was greater than 1.0 inches.Otherwise the board was classified as a “non-rogue”.

The initial data from lumber groups 1 and 3 were used to develop andtrain the classification algorithm and the initial data from boards ingroup 2 were used to test it. Five inputs were used to develop theclassification algorithm: initial absolute crook, initial absolute bow,ultrasonic velocity, initial moisture content and a measure of thevariability in board density. The boards from groups 1 and 3 wereassigned into the two groups, rogue and non-rogue, based on their finalabsolute crook and final absolute bow. Using this definition, there were92 rogues and 309 non-rogues in the training set, groups 1 and 3.

Linear discriminant analysis was used to develop a discriminant functionto classify the boards. The table below shows the percentage of boardsthat were correctly classified as rogue or non-rogue and those that wereincorrectly classified in the training set.

TABLE 1 True Group Put into Group Non-Rogue Rogue Non-Rogue 280 16 Rogue29 76 Total 309 92

Eighty-three percent, or 76 out of 92 rogues, were correctly classifiedas rogues. Ninety-one percent, or 280 out of 309 non-rogues, werecorrectly classified as non-rogues. FIG. 2 provides a plot of themisclassified boards.

The linear discriminant function developed on the training set was thenapplied to the test set of boards, group 2. This group had 62 boardsassigned as rogues and 143 assigned as non-rogues. The results of theclassification using the discriminant function are shown in the tablebelow.

TABLE 2 True Group Put into Group Non-Rogue Rogue Non-Rogue 135 12 Rogue8 50 Total 143 62

In this case, 50 of the 62 rogues were correctly classified with theinitial data as rogues, which translates to 81% accuracy. Also, 135non-rogues were correctly classified using the initial data asnon-rogues, which translates to 94% accuracy. A graph of themisclassified boards is shown in FIG. 3.

A special case of the methods described above may occur, for example,when the classes that are predicted are existing industry grade classesand an objective is to sort wood products into those grade classes.Another special case occurs when existing grades are not used, but thewood product is to be sorted into new classes developed based on aparticular use of the wood product. An example is classifying lumberinto categories including those that will warp significantly in dryclimates versus those that will not.

Estimates of the cost of misclassification can be used in the creationof the classification models or algorithms. For example, there may be ahigher cost associated with a rogue board being classified as anon-rogue, than there is for a non-rogue being classified as a rogue. Inthese cases, the models and/or algorithms can be developed using thesecosts in such a way as to minimize the occurrence of the costliermistake¹⁴. ¹⁴Ripley, B. D. (1996) Pattern Recognition and NeutralNetworks, Cambridge: Cambridge University Press.

Shrinkage Rate Coefficient as an Indicator of Dimensional Stability

Wood is a hygroscopic material that undergoes dimensional changes whenit experiences a change in moisture content. This phenomenon occurs on alocal (fiber) scale. The dimensional change that occurs with changes inmoisture content is due to drying or swelling forces in the wood.Dimensional changes in wood occur whenever there is a change in thedistribution of internal (or external) stresses. The degree ofmoisture-induced-shrinkage (and consequently, shrinkage-related stress)depends on several known factors, such as galactan content, micro-fibrilangle, specific gravity, MOE, and others. Many of these factors can bequantitatively or qualitatively evaluated with different types ofsensors. For example, MOE can be estimated from the propagation of soundthrough wood, and specific gravity can be estimated from the capacitanceof wood. The combined use of multiple sensors can then be used toestimate the moisture-induced shrinkage patterns in wood. The spatialresolution of the patterns depends on the spatial resolution of themeasurements.

The extent of moisture-induced dimensional change for a given piece ofwood depends on physical and chemical properties of the wood, as well asboth the magnitude of the moisture change and the values of the initialand final moisture contents. The shrinkage behavior of wood is commonlyexpressed as a shrinkage-coefficient (alternatively calledLSRC=Longitudinal Shrinkage Rate Coefficient); this is defined as

${LSRC} = \frac{\Delta\;{l/l}}{\Delta\;{MC}}$where l is the length of the wood segment, MC is the moisture content ofthe wood, and the Greek letter Δ is the familiar mathematical differenceoperator. This shrinkage-coefficient is a function of the moisturecontent.

Estimation of shrinkage-coefficient patterns from multiple sensors maybe achieved via a shrinkage-coefficient prediction equation and/oralgorithm, as well as inputs from the sensors to the equation oralgorithm. More than one shrinkage-coefficient prediction equationand/or algorithm may be utilized for each section of a wood product. Theestimation of shrinkage patterns in a piece of wood can be determinedfrom the appropriate shrinkage-coefficients and starting and endingmoisture states.

The inputs to a shrinkage model are functions of the sensor signals andmay be either quantitative or qualitative. For example, an input couldbe the estimated moisture content for each 12 inch lineal section of apiece of lumber, as estimated by a moisture meter. Another example is anindicator for the presence or absence of a knot in a 12 inch by 1 inchsection of wood, based on an RGB image. Inputs to the models may bedirect sensor measurements, pre-processed signals, or combined signalsfrom several sensors. Signal pre-processing may include, but is notlimited to, such steps as filtering, smoothing, derivative calculations,power spectrum calculations, Fourier transforms, etc., as is well knownin the art.

The shrinkage-coefficient prediction equation(s) and/or algorithm(s) areused to map the set of inputs to a real-valued number. There are manyforms of equations or algorithms that could be used, and a generalreference is Hastie, et al¹⁵. A common example is a linear model of theform,

${y_{j} = {\beta_{0} + {\sum\limits_{i}\;{\beta_{ij}x_{ij}}}}},$where y_(j) is the response variable (e.g., LSRC) and the set of inputsx_(ij) may be the inputs described above, or basis expansions of thoseinputs. Typically, the coefficients for such a model will not be knowna-priori, and may be determined from a training-set of data. Otherexamples of supervised learning procedures include regression trees,additive models, neural networks, penalty methods, and boosting methods.¹⁵Hastie, T., Tibshirani, R., and Friedman, J., (2001) The Elements ofStatistical Learning, Springer, N.Y.

The spatial resolution of the inputs will determine the spatialresolution of the shrinkage estimates. If the resolution of theshrinkage estimates is high enough, it is possible to estimate shrinkagepatterns throughout a piece of wood such as a board. In an embodiment,resolution required for a 2×4 piece of lumber may be 12 inches (long)×¾inch (wide)×¾ inch (thick), although any practical level of resolutionis possible. The section of board over which a prediction is made is acoupon. The pattern of coupon shrinkage estimates can be used torepresent the shrinkage patterns in a wood product.

Two general types of shrinkage estimates may be used: ‘absolute’shrinkage estimates which predict, for example, a shrinkage value foreach coupon-level piece of a board; and ‘differential’ shrinkageestimates which predict a shrinkage difference between a coupon and areference coupon.

Localized moisture content changes in wood may occur, for example, whenthere is a change in the ambient RH conditions, or when moisture-contentnon-uniformities in the wood are allowed to equilibrated. The estimatedshrinkage patterns—either absolute or differential—can then be used toestimate the moisture-induced dimensional changes in the wood product.This could be accomplished, for example, by using the patterns ofshrinkage estimates as inputs to a finite element model, although otheroptions exist.

The following example illustrates how information from multiple sensorswas used to estimate the dimensional change in wood due to a change inambient relative humidity.

EXAMPLE 2

The sensor data used were “Tracheid-effect” line images and absorbancespectra obtained from near infrared (NIR) spectroscopy. (Additionalinformation describing these two sensor technologies can be found in(Nystrom and Hagman)¹⁶ and (Williams and Norris)¹⁷ respectively). Atraining data set consisting of approximately 350 12″×1″×¾″ pieces ofwood was used to build a shrinkage-coefficient calibration model. Eachpiece of wood was scanned for both Tracheid-effect images and NIRspectra. Several parameters were calculated from each Tracheid-effectimage. In addition, each piece of wood was equilibrated at two differenttimes in two different relative humidity environments—20% RH and 90% RH.Length measurements were made at each humidity condition and themoisture-induced dimensional change was recorded. ¹⁶Nystrom, J.; Hagman,O.; Methods for detecting compression wood in green and dry conditions,Proceedings of the SPIE—The International Society for OpticalEngineering (1999) vol. 3826, p. 287-94.¹⁷Williams, P., Norris, K.(editor), (2001) Near-Infrared Technology in the Agricultural and FoodIndustries, Second Edition, American Association of Cereal Chemists, St.Paul, Minn.), 312 pp.

A prediction model for dimensional change was developed based onfirst-principle considerations using Tracheid-effect parameters and NIRspectra as inputs. The prediction equation used isLSRC=β₀+β₁·D+β₂·R+β₃·R·D, where LSRC is the moisture-induced length-wisedimensional change of each piece of wood, the β's are regressioncoefficients estimated from the training dataset, D is the ‘exponentialdecay’ (rate of decay of the intensity as a function of distance fromthe projected light-source) of the tracheid-effect line intensity, and Ris the ratio of two NIR absorbance values, A1700/A1650. The calibrationplot for a differential shrinkage-coefficient model is shown in FIG. 4.

Following the calibration of the shrinkage-coefficient model, 23 8-foot2″×4″ boards were scanned for both tracheid-effect images and NIRspectra. These pieces of wood had already been cycled through tworelative humidity environments, and the change in crook and bow wererecorded on each piece. The parameters calculated from thetracheid-effect and NIR data were used as inputs to the differentialshrinkage-coefficient model to produce a map of differentialshrinkage-coefficient values for each piece of lumber. A shrinkage mapwas calculated from the shrinkage-coefficient estimates and the targetmoisture contents. The shrinkage map was then input to a finite elementmodel (DIMENS) to predict the change in warp-profile of each piece oflumber. The predicted change in crook is plotted against the measuredchange in FIG. 5.

The previous example illustrates the prediction of moisture-inducedcrook-change from estimated shrinkage maps using a finite element model.Similar methods can be used for cup and bow. Analogous methods can beused to predict moisture-induced twist from estimated grain-angle, pithlocation and possibly other variables.

Residual stress arises only in the presence of shrinkage differences,noting that uniform shrinkage is an indication of no residual stresspresent in a sample. Thus, it is proposed that there should be a strongrelationship between residual longitudinal stress and longitudinalshrinkage differences, rather than between residual longitudinal stressand longitudinal shrinkage itself. This requires a scan for residualstress when the nearby shrinkage is different, not just when the localshrinkage is relatively high.

During the manufacture of lumber, it is sometimes desired to rip a piecein order to generate 2 or more narrow pieces whose combined value isgreater than the wider parent. If there are residual stresses in theparent board, those stresses might be relieved during this rippingoperation causing the ripped pieces to spring outward and undergo addedundesirable warp distortion. Thus, there is a need to understand whetheror not this potential exists in a parent piece of lumber before a ripdecision is made. Estimates of longitudinal shrinkage patterns can beused for this purpose as illustrated by the following example.

EXAMPLE 3

Eighteen 2×4 cross sections were equilibrated to 20% RH and ripped intofour equal coupons. The instantaneous strain of each coupon wasdetermined from the difference in length before and after ripping. Alongitudinal shrinkage rate coefficient (LSRC) was also determined foreach coupon. Two pairs of coupons on either side of centerline werereviewed. Data from these pairs was analyzed to determine whetherpredicted LSRC differences (based on methods described earlier) could beused to identify pairs having high instantaneous strain difference (i.e.sections likely to distort during a ripping operation.)

Results are shown in FIG. 21. The test demonstrated that LSRC estimatescan indeed be used to identify pieces of lumber that likely containsignificant internal stresses and are, therefore, not candidates for aripping operation.

The method can be applied to a board that has residual moisturegradients resulting from kiln-drying and that will subsequently changeshape as the internal moisture equilibrates both within the piece(moisture leveling) and to its external environment. If the subsequentshape change is large enough, such a board may no longer meet the warplimits for its designated grade.

Shape change may be predicted according to the above method using thepredicted shrinkage-coefficients for each coupon within the board,together with the anticipated moisture content change of each coupon. Ifthe final state is one of uniform, equilibrated moisture content, thenthe moisture content changes of the coupons will not all be the same ifthere initially are moisture gradients within the board. In the method,the moisture content change for each coupon may be determined from theinitial moisture content distribution and the final target moisturecontent. The moisture content change is then multiplied by thecorresponding longitudinal shrinkage rate coefficient determined for thecoupon. The resulting coupon shrinkage values are processed using, forexample, a finite-element and/or an algebraic warp prediction model todetermine the anticipated warp changes due to leveling and equilibrationof the initial moisture gradients. The predicted warp changes arefinally added to the initial warp values of the board to determinewhether or not the final shape of the piece will exceed any of the warplimits for its designated grade.

An example of the above-described method is provided below:

EXAMPLE 4

The anticipated crook changes of three 8-ft. 2 inch×4 inch boards(B4-179, D4-175, and B4-59) were determined for several differenthypothetical moisture content leveling and equilibration scenarios.Three different initial moisture content profiles, as previouslymeasured in kiln-dried lumber, were used and the final equilibriummoisture content was assumed to be 12%. The longitudinal shrinkage ratecoefficients of the coupons within the three boards were determinedusing the above-described methods. FIG. 6 illustrates different initialmoisture content profiles and FIG. 7 illustrates predicted crook changesfor each profile. The predicted crook change for each board is added toits actual crook at its initial moisture content condition in order todetermine whether or not the crook at the final moisture contentcondition would exceed the crook limit for the designated grade of theboard.

B. Methods of Combining Measurements of Surface Moisture Patterns with aMeasurement of Bulk (Average) Moisture to Estimate Moisture Gradientsand Patterns Within a Wood Product

At the end of kiln drying, the moisture content in each piece of lumberis typically distributed in a non-uniform manner, with relatively highermoisture contents near the core of the piece and lower moistures at andnear the surfaces. This activity is illustrated in FIG. 8. Such patternsmay not be symmetric in cross-section, with edge-to-edge andface-to-face differentials. The patterns may vary along the length ofthe board, typically with relatively lower moisture contents near eachend. Prior testing has shown that such moisture patterns persist in thelumber for weeks after drying, and thus will often remain at the time ofplaning.

Because of such moisture variability, board warp profile predictions ofthe kind described above may require an estimate of the moisture contentof each shrinkage coupon. These estimated moisture content values may beused together with the specified final target moisture content todetermine the moisture content changes for which the warp change of theboard must be predicted.

At any location along the length of a board, the surface moisturecontent profile and the corresponding average moisture content may becombined to obtain an estimate of the moisture content for eachshrinkage coupon in that length section. An estimated moisture contentis determined for each shrinkage coupon position using a linear modelthat employs the average moisture content of the corresponding boardsection (for example, from an NMI meter) and the surface moisturecontent for that coupon position (for example, from anelectrical-resistance pin-type moisture meter). The moisture contentestimate model is of the general form:MC _(ij) =k0_(i) +k1_(i) *A _(j) +k2_(i) *S _(ij)where

-   -   MC_(ij) is the estimated moisture content of the “i”th shrinkage        coupon in the “j”th board section (generally there would be 8        coupons per section)    -   k values are constants but may have different values for each        shrinkage coupon position “i”    -   A_(j) is the average moisture content of the “j”th section    -   S_(ij) is the surface moisture content of the “i”th shrinkage        coupon in the “j”th board section.

In general, there would be a different set of k values associated witheach board width.

FIG. 9 illustrates results from a test of the claimed method. In thattest, it was shown that when combining both the average moisture contentand the surface moisture content pattern, the error of the prediction ofcoupon (element) moisture content was reduced from 1.7% to 1.3% mc(RMSE), as compared to predictions based on the average moisture contentalone.

Near Infrared (NIR) absorbance spectroscopy techniques can be used tomeasure the moisture content of materials. There are many examples knownto those skilled in the art demonstrating the basic method for manybiological materials, including wood. In most examples, the material isground and thus relatively homogeneous with the surface and interiorhaving similar moisture contents.

In wood this may not be the case. Water has several absorption bands inthe NIR region. Due to the strength of these absorption bands and theoptical density of wood, the NIR reflectance spectrum at the waterabsorption bands is a measure of the surface moisture (within a fewmillimeters of the surface). If full NIR spectrum methods are used, asingle NIR reflectance spectrum can be used in both surface moisture andshrinkage prediction models. If discrete wavebands, or ratios ofdiscrete wavebands, are used, then it is likely that the NIR wavebandsselected for surface moisture prediction models will be different fromthose used to model shrinkage.

The most common NIR models for moisture are multiple linear regressionmodels of second derivative spectra at a few (typically three or less)wavebands. However, full spectrum models, or models using ratios ofabsorbance values or ratios of derivative values can also be used. Usingthese methods, NIR spectral data are analyzed to determine and assign asurface moisture content for each shrinkage coupon.

The amount of light absorbed by water varies from water absorbance bandto band. In general, the longer the wavelength the more light that isabsorbed for the same water content. Thus, by selecting the wavelengthfor water measurement, one can control to some degree the depth ofpenetration of the light into the material. Thus, there would be morepenetration into the wood at the 960 nm water band than at the 1910 nmwater band. If one was interested in the surface moisture content, thenlonger wavebands like 1910 nm should give a measure closer to thesurface, while 960 nm should give an average moisture content to agreater depth. Such measurements may be taken by, for example, devicesor systems such as a Kett High Moisture NIR meter (model number KJT100H)manufactured by Kett Corporation.

A number of the bulk properties of wood are affected by its moisturecontent. For example, below the fiber saturation point, both the modulusof elasticity (MOE) and the electrical resistance increase withdecreasing moisture content. Such relationships form the basis for avariety of moisture measurement methods including, for example,dielectric, electrical resistance, and nuclear magnetic resonance. Thesemethods are employed in various commercial lumber moisture measurementsystems, such as those made by Wagner and NMI (dielectric), and byDelmhorst (electrical resistance). In both the Wagner and NMI planermoisture meters, the lumber passes over a capacitance-measuring plateand the average, or bulk, moisture content of the wood in themeasurement zone is determined by its dielectric properties. Suchstate-of-the-art planer moisture meters are not yet able to resolve thecross-sectional variability in moisture content with a resolution on theorder of the shrinkage coupon dimensions. They provide a cross-sectionalaverage moisture content that is characteristic of a short lengthsection of the board. That average moisture content can be used with anNIR-based estimate of moisture content variation over the surface of theboard to estimate the moisture gradients and patterns within the board,following the above-described method.

C. Methods of Estimating the Dimensional Stability of a Wood Productfrom Simple Algebraic Differences in Moisture, Shrinkage Rates and GrainAngles Observed on Outer Surfaces

Finite-element modeling of lumber warp behavior has shown that crook andbow stability are governed almost entirely by the pattern of variationin the lengthwise shrinkage within the piece. Specifically,differentials in lengthwise shrinkage across the width largely determinecrook, while differentials across the thickness are responsible for bow.Furthermore, it has been discovered that the quantitative relationshipbetween crook or bow stability and lengthwise shrinkage can beestablished using relatively simple mathematical operations, rather thanmore sophisticated and complicated finite-element modeling methods. Inparticular, the curvature of any board length-segment or section,expressed as the second derivative of the crook or bow profile, can bedetermined from a linear combination of the shrinkage values of thecoupons comprising that segment or section. The overall crook or bowprofile of the board can be determined from a section-by-sectiondouble-integration of those second derivative values.

To determine crook, each board segment must be divided into at least 2shrinkage coupons across the width. In general, better results may beobtained when each board segment is divided into at least 4 couponsacross the width. If a board segment is divided into four shrinkagecoupons, having shrinkage values T1, T2, T3, and T4, then the crookresulting from that shrinkage will exhibit a curvature over that segment(expressed as the second derivative of the board's edge profile) thatcan be determined by a linear combination of the general form:C″=k1(T1−T4)+k2(T2−T3)+k3where

-   -   C″ is the second derivative of the crook profile along the edge        of the board    -   k values are constants but may have different values for each        board width    -   T values are coupon shrinkage values that are determined by the        product of the corresponding longitudinal shrinkage rate        coefficient (LSRC) and moisture content change (MC):        Ti=LSRCi×MCi

This method was tested in the following example:

EXAMPLE 5

Finite-element model predictions were made for crook in 138 differentexamples of 8-ft. 2×4 boards. Each of these example boards was dividedinto 6 length segments and each length segment was divided into 8shrinkage coupons, using a 4×2 configuration, namely, with four couponsacross the width by two coupons through the thickness. The shrinkagevalues for each pair of coupons at each width location were averaged togive four shrinkage values across the width, per the above equation. Thesecond derivative of the predicted crook profile was calculated for eachboard segment, and a least-squares regression was used to determine thecoefficients (k) in the equation above. FIG. 10 illustrates a plotcomparing the second derivative values calculated using that equation(C″) with the corresponding second derivative values calculated from thecrook profiles predicted by the finite-element model, and showsexcellent agreement.

To predict the crook of a board, the second derivative values calculatedusing the above equation (C″) are integrated twice to yield the actualedge profile of each board segment. This method was tested using couponlongitudinal shrinkage rate coefficients determined for 23 8-ft. 2×4boards. First, the second derivative values for each length segment werecalculated using the above equation, then those derivative values wereintegrated twice to determine the crook profile of each of the 23boards. The resulting crook values are compared to the correspondingcrook values predicted using the finite-element model, and showexcellent agreement in FIG. 11.

To determine bow, each board segment must be divided into at least 2shrinkage coupons through the thickness. If a board segment is dividedinto two shrinkage coupons, having shrinkage values T1 and T2, then thebow resulting from that shrinkage will exhibit a curvature over thatsegment (expressed as the second derivative of the board's face profile)that can be determined by a linear combination of the general form:B″=k1(T1−T2)+k2where

-   -   B″ is the second derivative of the bow profile along the face of        the board    -   k values are constants but may have different values for each        board width    -   T values are coupon shrinkage values that are determined by the        product of the corresponding longitudinal shrinkage rate        coefficient (LSRC) and moisture content change (MC):        Ti=LSRCi×MCi

This method was tested in the following example:

EXAMPLE 6

Finite-element model predictions were made for bow in 138 differentexamples of 8-ft. 2×4 boards. Each of these example boards was dividedinto 6 length segments and each length segment was divided into 8shrinkage coupons, using a 4×2 configuration, namely, with 4 couponsacross the width by two coupons through the thickness. The shrinkagevalues for each set of 4 coupons at each face were averaged to give twoshrinkage values through the thickness, per the above equation. Thesecond derivative of the predicted bow profile was calculated for eachboard segment, and a least-squares regression was used to determine thecoefficients (k) in the equation above. The plot in FIG. 12 compares thesecond derivative values calculated using that equation (B″) with thecorresponding second derivative values calculated from the bow profilespredicted by the finite-element model, and shows excellent agreement.

To predict the bow of a board, the second derivative values calculatedusing the above equation (B″) are integrated twice to yield the actualface profile of each board segment. This method was tested using couponlongitudinal shrinkage rate coefficients determined for 23 8-ft. 2×4boards. First, the second derivative values for each length segment werecalculated using the above equation. Then, those derivative values wereintegrated twice to determine the bow profile of each of the 23 boards.The resulting bow values are compared to the corresponding bow valuespredicted using the finite-element model, showing excellent agreement inFIG. 13.

D. Methods of Estimating the Shrinkage and Grain Angle Properties ofWood by Interpreting the Intensity Pattern that is Diffusely Reflectedfrom a Surface Illuminated by a Light Source (Laser or Non-Laser)

The tracheid-effect in wood is known (see, for example Nystrom, 2003).When a wood surface is illuminated by a point or line light source, thepatterns of diffuse reflectance are influenced by the physical andchemical properties of the wood. Metrics or parameters calculated fromthese patterns may be used to estimate physical properties of the wood,such as, for example, shrinkage and grain-angle properties.

Many types of parameters may be calculated from the diffuse reflectancepatterns. When the diffuse-reflectance is focused to an area arraycamera, the grayscale pattern of the resulting image may be analyzedwith standard or non-standard image analysis techniques, as is wellknown in the art. An example of a grayscale image from aline-light-source is shown in FIG. 14. Examples of some standard imageanalysis metrics include size of area formed between two grayscalethresholds, and convex hull area of an image.

Statistical and mathematical parameters may also be calculated frompatterns of diffuse reflectance. For example, the rate of decay of theintensity as a function of distance from the projected light-source mayrelate to the dimensional stability of wood. There are many differentmodels for estimating the rate of decay. A common model islog(intensity)=A+kx, where x is the distance from the projected lightsource, and A and k are model parameters. Examples of other models aredescribed in Bates and Watts, 1988. It has been empirically noted thatthe rate of decay of diffusely reflected light intensity may berepresented by a combination of exponential-decay processes. Thebi-exponential process can be represented by the equation: E(y_(i))=φ₁exp(−φ₂x_(i))+φ₃ exp(−φ₄x_(i)), φ₂>φ₄>0. The estimated parameters fromthe exponential decay processes may reflect different wood propertiesand could each be used as inputs to a shrinkage model. FIG. 15 showsseveral examples of the bi-exponential model fit to tracheid-effect lineimages.

Parameters, such as those related to the rate of decay of lightintensity, may be estimated on either ‘side’ of the light image or bycombining information from each side. Empirical evidence also suggeststhat a comparison of decay rates on the ‘left’ and ‘right’ side of alight source may provide useful predictive information.

When the light source is a spot, other parameters may be computed fromthe diffuse reflectance patterns. A spot light source typically makes anellipse pattern on the surface of wood. Parameters such as the ellipseratio, ellipse orientation, and ellipse angle may be calculated, asdiscussed in (Zhou and Shen, 2002). The surface grain angle may beestimated from the ellipse angle.

The physical properties of wood that influence the tracheid-effect maybe local in nature. The spatial resolution of estimates based on thecalculated parameters will then depend on the frequency of sampling thelight intensity patterns. The various attributes computed from theintensity patterns can be used as inputs to a shrinkage predictionequation or algorithm. Such an equation maps the set of inputs to areal-valued number. There are many forms of equations or algorithms thatcould be used, and a general reference is Hastie, et al. The followingexample illustrates how information from a laser line image was used toestimate longitudinal shrinkage rate coefficients of wood:

EXAMPLE 7

A training dataset consisting of approximately 350 12″×1″×¾″ pieces ofwood was used to build a shrinkage-coefficient calibration model. Eachpiece of wood was scanned with a Tracheid-effect line image and aside-spot image. Several parameters were calculated from eachTracheid-effect image. In addition, each piece of wood was equilibratedat two different times in two different relative humidityenvironments—20% RH and 90% RH. Length measurements were made at eachhumidity level and the moisture-induced length change was recorded.

A prediction model for dimensional change was developed usingtracheid-effect parameters as inputs. The prediction equation wasconstructed using multivariate-adaptive-polynomial-spline-regression.Five main terms were included in the model: ‘Right’ decay parameter,mean Ellipse ratio, convex-hull-area-height, mean-angle, and thewithin-piece standard deviation of the ratio of the ‘right’ and ‘left’decay parameters. In addition, 3 spline-knots and the interactionbetween ‘right’ decay and mean-angle were included in the model. Thecalibration plot for a differential shrinkage-coefficient model is shownin FIG. 16.

The previous example illustrated the prediction of woodshrinkage-coefficients from parameters calculated from bothline-intensity and spot-intensity images. Analogous methods can be usedto predict grain-angle from both line and spot images.

E. Methods of Using Multiple Sensors (Sensor Fusion) to Infer Crook andBow Directly

Crook and bow result from dimensional instability in a piece of wood.Many factors are known to be associated with the dimensional stabilityof wood. For example, wood with high MOE is generally dimensionallystable, while wood with large amounts of compression-wood is typicallyunstable and prone to crook or bow. Moisture-induced dimensionalinstability is a result of moisture-induced shrinkage patterns in a woodproduct, such as a piece of lumber. One approach to estimatingdimensional change, discussed above and illustrated in Example 2, firstestimates the shrinkage-coefficient patterns in a piece of wood, thenuses these shrinkage-coefficient patterns to predict crook or bowresulting from a change in moisture content using, for example, a finiteelement model. This can be thought of as a two-step approach to warpprediction wherein a first step is to predict shrinkage, and a followingstep is to predict warp.

Another approach is to directly predict the crook or bow of a piece ofwood using data from multiple sensors and a single prediction model oralgorithm. Using this approach, the prediction model or algorithm mayuse inputs of many different resolution scales. The model inputs arefunctions of the sensor signals and may be either quantitative orqualitative. For example, an input could be the estimated averagemoisture content for the entire piece of wood, as estimated by amoisture meter. Another example is an indicator for the presence orabsence of a knot in a 12″ by 1″ section of wood, based on an RGB image.Inputs to the models may be direct sensor measurements, pre-processedsignals, or combined signals from several sensors. Signal pre-processingmay include, but is not limited to, such steps as filtering, smoothing,derivative calculations, power spectrum calculations, Fouriertransforms, etc., as is well known in the art.

The crook or bow prediction equation(s) and/or algorithm(s) are used tomap the set of inputs to a real-valued number. There are many forms ofequations or algorithms that could be used, and a general reference isHastie, et al. Typically, the model or algorithm parameters will not beknown a-priori, and must be determined from a training-set of data. Thefollowing example illustrates how information from multiple sensors wasused to directly estimate the dimensional change in wood due to a changein ambient relative humidity.

EXAMPLE 8

Three units of lumber, each containing approximately 200 8-foot 2×4boards were obtained from a mill. Each piece of lumber was measured atthe mill for crook, bow, average moisture content, acoustic velocity andspecific gravity. Each piece of wood was then placed in a 20% RHenvironment for 5 weeks and then measured again for crook and bow. Inthis example, the objective was to estimate the final crook or bow (at20% RH) using the initial data from multiple sensor groups. Three inputswere used to develop an absolute-crook prediction model: initialabsolute crook, acoustic velocity, and initial moisture content. Asimple linear regression model with these inputs was trained on twounits of lumber. The calibration plot for absolute-crook at 20% RH isshown in FIG. 17.

F. Methods of Rapidly Simulating “In-Service” Warp Distortion of a WoodProduct and/or Rapidly Estimating Shrinkage Properties of a Wood Productby Using Electromagnetic Energy to Dry and Redistribute Absorbed Water

Hygroscopic materials, such as wood, absorb or release an amount ofmoisture needed to reach equilibrium with the surrounding environment.Consequently, most wooden materials will undergo significant moisturechange between the time they are manufactured and when they reach finalequilibrium after put into service. Typical interior equilibriummoisture levels in the United States vary by geography and season withaverage values ranging from 6% in the desert Southwest to 11% along theGulf Coast. (Wood Handbook²). Once wood is placed in a new environmentit takes approximately 6 weeks to reach a new equilibrium moisturecondition. Until that equilibrium state is reached, moisture gradientsexist from the inside to the outside of a piece of wood.

An objective of the present invention is to predict how straight anindividual piece of lumber will be after it reaches a final equilibriumstate, i.e., where no moisture gradients exist. This prediction relieson estimating lengthwise shrinkage patterns within the piece of lumberand then interpreting how those shrinkage patterns interact to causewarp. In order for this technology to be applied, quality controlprocedures may be required to ensure that the “in service” warpprediction is accurate. Such procedures must be capable of providingrapid feedback on the accuracy of estimates of bothshrinkage-coefficients and resulting distortion. The long time requiredfor a wooden piece to reach moisture equilibrium presents a problem tothe development of operationally feasible quality control methods. Toresolve this problem, it is proposed to utilize electromagnetic energyto accelerate the rate at which a wood product reaches a new equilibriummoisture.

Electromagnetic energy is efficiently absorbed by polar molecules suchas water. When wood is placed in a microwave or radio frequency field,the energy is preferentially absorbed by regions having higher moisture.As a result, water in these high absorbing regions rapidly migrates tolower moisture regions, thereby leveling the moisture gradients. Thisprocess can, therefore, be used on wood to quickly achieve a newmoisture state that emulates in-service equilibrium in which moisturegradients are minimized.

This method can be used to validate both shrinkage-coefficientpredictions and warp of full size pieces. The method can be used toemulate shrinkage or in-service distortion resulting from moistureleveling or moisture loss. To emulate distortion resulting from moistureleveling, the piece must be wrapped in a moisture barrier before it isplaced in an electromagnetic field. Electromagnetic energy in thefrequency range of, for example, 13.6 MHz (RF) to 2.45 GHz (microwave)can be used in this method. This full range can be used to acceleratethe process of determining shrinkage-coefficients of small samples (lessthan 50 cubic inches); whereas the RF portion of the spectrum ispreferred for inducing warp in full size lumber samples. In anembodiment, the wood product is dried to a moisture content which isless than 20%.

In an embodiment, a method is provided for confirming a warp distortionprediction (i.e., quality control) for a wood product. The methodcomprises the steps of: obtaining an initial moisture pattern for thewood product; predicting warp distortion of the wood product based onthe initial moisture pattern; placing the wood product in an environmentwherein the wood product is subject to electromagnetic energy; applyingsufficient electromagnetic energy to the wood product to change itsmoisture content to a second level wherein the moisture content has asecond value equivalent to an expected long term in-service equilibriumvalue; measuring warp distortion of the wood product at the secondmoisture level; and comparing the predicted warp distortion to the warpdistortion at the second moisture level.

The following example describes an experiment conducted to comparelongitudinal shrinkage rate coefficients determined by RF dryingcompared to conventional conditioning in a controlled environment:

EXAMPLE 9

A set of candidate wood specimens was equilibrated (size approximately½″ thick×1″ wide×12″ long) in 65% relative humidity for at least 3weeks. 30 representative samples were selected from the equilibratedgroup. The weight and length of each specimen were measured. Eachspecimen was dried to approximately 5% moisture using RF dryer (dryingdone on approximately 5 minute cycle using a 20 KW 40 MHz dryer at RadioFrequency Company, Millis Mass.). The weight and length of each specimenwas re-measured. The acquired data is used to estimate longitudinalshrinkage rate coefficients (LSRC₁) using the formula:LSRC ₁=length change÷initial length÷moisture content change

Next, the RF dried coupons were re-conditioned in 20% RH. The weight andlength of each specimen were re-measured. This data was used tore-estimate longitudinal shrinkage rate coefficients (LSRC₂). Acomparison was made between shrinkage-coefficient estimates LSRC₁ andLSRC₂. The results are plotted in FIG. 18 and show excellent agreementbetween the conventional and accelerated methods of estimatingshrinkage-coefficients.

G. Methods of Using Multi-Sensor Data to Estimate the ShrinkageProperties of Wood by First Using the Multi-Sensor Data to Identify theType or Class of Wood that is Being Evaluated, and then Using the MultiSensor Data to Estimate Shrinkage Using a Class-Specific Equation and/orAlgorithm

Parameters calculated from multiple sensors, such as tracheid-effectline images and spectroscopy data, have shown to be useful in predictingthe shrinkage properties of wood. Many of the parameters found to beassociated with shrinkage are also influenced by chemical or physicalfeatures of the wood that may or may not be associated with shrinkage.For example, wood that contains pitch may be more prone tomoisture-induced dimensional instability than typical clear-wood.However, both tracheid-effect images and certain spectral bands aregreatly influenced by pitch in ways very different fromnon-pitch-containing wood with similar shrinkage properties. FIG. 19shows two spectra. The “top” spectra is from a sample containing pitch,the other from a sample that does not contain pitch. Both wood sampleshave similar shrinkage behavior; however there are several importantdifferences between these spectra, including a sharper peak at 1200 nmand a steeper rise between 1650 and 1700 nm in the pitch-containingspectrum. These spectra are typical of other pitch and non-pitchcontaining southern-pine samples.

This suggests that improved shrinkage estimates could be obtained byhaving different models or algorithms for different types of wood. Sucha strategy can be accomplished with a two-step approach to shrinkageprediction. First, the wood-type of a region of interest is identifiedusing inputs from one or more sensors (Classification Step). The type ofqualitative assessment may be done with respect to a dimensionalstability property, or other property. For example, the dimensionalstability property which enables classification may be crook. In anotherembodiment, the property allowing classification may be “pithcontaining”. Second, a class-specific shrinkage prediction model oralgorithm is applied based on the results of the first step (this secondstep can be referred to as a Prediction Step). Examples of wood typesinclude, but are not limited to, knots, compression-wood, pitch,pith-containing, early-wood, late-wood, species and blue-stain. Themodels or algorithms to classify regions of interest or to predictshrinkage behavior will typically be learned from a training set ofdata. Methods for classification and prediction have previously beendiscussed.

The classification-step will predict membership into any of K+2categories, where K is the number of named classes (e.g., knots). Theother two categories are for “outliers”, namely, cases which do not looklike others that have been observed, and “doubt”, namely, cases in whichclass membership is too uncertain to make a decision. Example 10describes a two-step approach to estimating shrinkage properties usingmulti-sensor data.

EXAMPLE 10

In this example, the data used were Tracheid-effect line images and NIRabsorbance spectra. A training dataset consisting of approximately 35012″×1″×¾″ pieces of wood was used to build a shrinkage-coefficientcalibration model. Each piece of wood was scanned for bothtracheid-effect and NIR absorbance data. Several parameters werecalculated from each Tracheid-effect image. In addition, each piece ofwood was equilibrated at two different times in two different relativehumidity environments: 20% RH and 90% RH. Length measurements were madeat each humidity level and the moisture-induced dimensional change wasrecorded.

A partial least squares model was trained on all cases using only theNIR absorbance data. FIG. 20 illustrates two plots of results. Theleft-hand plot shows the measured shrinkage values plotted against thefitted values of all cases. The ratio of NIR absorbance values at 1200nm and 1270 nm has been found to be a useful indicator for the presenceof pitch. If the ratio A1200/A1270 is greater than 1.18, the samplelikely contains pitch. Samples with this ratio greater than 1.18 arehighlighted in the left-hand plot. The fit of these samples is ratherpoor. A second set of models was then developed; one only on sampleswith A1200/A1270 greater than 1.18, and one only on samples with thisratio less than 1.18. The right-hand plot in FIG. 20 shows the predictedresults using class-specific models. That is, samples with A1200/A1270greater than 1.18 were predicted with the model trained on the“pitch-containing” samples, while the samples with A1200/A1270 less than1.18 were predicted with the model trained on the “non-pitch-containing”samples. The results show that the fit of the ‘pitch-containing’ samplesis improved. The fit of the samples with the ratio less than 1.18 isalso improved, although to a smaller extent than for the samples withthe ratio greater than 1.18.

In other examples of the two-step prediction approach, particularly forthe “outlier” or “doubt” categories, an option for the prediction-stepwould be to simply estimate the shrinkage value of a coupon from theaverage value of its neighbors. Alternatively, data from sub-regionswithin a coupon that have been labeled as an outlier or with doubt couldbe excluded from data aggregation (i.e., ‘masked’).

In an embodiment, a first algorithm may be provided for classifying theregion of interest into a category within a plurality of categoriesdirected to qualitative assessments of dimensional stability. A secondalgorithm may be provided for obtaining a quantitative estimate ofdimensional stability. This second algorithm may have a set of factors,such as for example A, B, C, and D which represent different equations,respectively. A calculation performed by the second algorithm may becontingent on the classification performed via the first algorithm. Forexample, if via the first algorithm, the wood product is classified intoa “pitch” category, factor “B” may default to zero, or some other valueand/or formula. In another example, if via the first algorithm, the woodproduct is classified as “pith-containing”, factor “D” and/or factor “C”may default to zero or other value, or be changed to another formula.Other variations based on classifications are also contemplated and maybe understood by those skilled in the art.

While the embodiments of the invention have been illustrated anddescribed, as noted above, many changes can be made without departingfrom the spirit and scope of the invention. Accordingly, the scope ofthe invention is not limited by the disclosure of the embodiments.Instead, the invention should be determined entirely by reference to theclaims that follow.

1. A method for determining crook potential of a wood product, themethod comprising the steps of: dividing the wood product into sections;dividing the sections into shrinkage coupons; obtaining a secondderivative of a crook profile for each section of the wood product,where each second derivative is a function of the shrinkage values ofthe shrinkage coupons within the corresponding section: C″=f(T1, T2, T3,. . . , Tn) wherein C″ is the second defivative of the crook profile foreach section of the wood product T values are the coupon shrinkagevalues for the n coupons into which the section is divided, and aredetermined by the product of a corresponding shrinkage rate coefficient(S) and a moisture content change (MC): Ti=Si.times.MCi; and integratingC″ twice to determine the crook profile of each section of the woodproduct.
 2. The method of claim 1 wherein the section is divided into atleast two shrinkage coupons across a width of the wood product.
 3. Themethod of claim 1 wherein a single sensor group examines each section.4. The method of claim 3 wherein the single sensor group performs ameasurement selected from the group consisting of: moisture contentmeasurement, electrical property measurement, structural propertymeasurement, acousto-ultrasonic property measurement, light scatter(tracheid-effect) measurement, grain angle measurement, shapemeasurement, color measurement, spectral measurement and defect maps. 5.The method of claim 1 wherein two or more sensor groups examine eachsection.
 6. The method of claim 5 wherein the two or more sensor groupsperform at least two measurements selected from the group consisting of:moisture content measurement, electrical property measurement,structural property measurement, acousto-ultrasonic propertymeasurement, light scatter (tracheid-effect) measurement, grain anglemeasurement, shape measurement, color measurement, spectral measurementand defect maps.
 7. A method for determining bow potential of a woodproduct, the method comprising the steps of: dividing the wood productinto sections; dividing the sections into shrinkage coupons; obtaining asecond derivative of a bow profile for each section of the wood product,where each second derivative is a function of the shrinkage values ofthe shrinkage coupons within the corresponding section: B″=g(T1, T2, T3,. . . , Tn) where B″ is the second derivative of the bow profile foreach section of the wood product T values are the coupon shrinkagevalues for the n coupons into which the section is divided, and aredetermined by the product of a corresponding shrinkage rate coefficient(S) and a moisture content change (MC): Ti=Si.times.MCi; and integratingB″ twice to determine the bow profile of each section of the woodproduct.
 8. The method of claim 7 wherein the section is divided into atleast two shrinkage coupons across a thickness of the wood product. 9.The method of claim 7 wherein a single sensor group examines eachsection.
 10. The method of claim 9 wherein the single sensor groupperforms a measurement selected from the group consisting of: moisturecontent measurement, electrical property measurement, structuralproperty measurement, acousto-ultrasonic property measurement, lightscatter (tracheid-effect) measurement, grain angle measurement, shapemeasurement, color measurement, spectral measurement and defect maps.11. The method of claim 7 wherein two or more sensor groups examine eachsection.
 12. The method of claim 11 wherein the two or more sensorgroups perform at least two measurements selected from the groupconsisting of: moisture content measurement, electrical propertymeasurement, structural property measurement, acousto-ultrasonicproperty measurement, light scatter (tracheid-effect) measurement, grainangle measurement, shape measurement, color measurement, spectralmeasurement and defect maps.